Problem: A circle with circumference $12\pi$ has an arc with a $210^\circ$ central angle. What is the length of the arc? ${12\pi}$ ${210^\circ}$ $\color{#DF0030}{7\pi}$
Answer: The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360^\circ} = \dfrac{s}{c}$ $\dfrac{210^\circ}{360^\circ} = \dfrac{s}{12\pi}$ $\dfrac{7}{12} = \dfrac{s}{12\pi}$ $\dfrac{7}{12} \times 12\pi = s$ $7\pi = s$